发表机构
Indian Institute of Technology Jammu; Fudan University; Bauhaus-Universität Weimar; Leibniz University Hannover（印度技术学院詹穆分校; 复旦大学; 魏玛包豪斯大学; 汉诺威莱布尼茨大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种机理分辨的相场断裂方法，将本构作为可替换算子，通过通道不变量分离纤维机制，并认证可容许性，在IM7/8552壳体上验证了纤维取向和曲率对损伤的影响。
AI 中文摘要
纤维增强壳体中的相场断裂模型通常针对单一闭式存储能进行公式化，因此应力、一致切线和平面应力凝聚仅针对该表达式进行推导和验证。在此，本构定律改为作为可替换算子进入。几何精确的Reissner-Mindlin壳体的Green-Lagrange应变通过参考度量的Cholesky因子拉回，并在四个相互正交的不变量上解析，具有精确的闭式恒等式，使得纤维、纤维间和相互作用通道的分离成为基变换而非建模假设。在弯曲的中面上，度量、Cholesky因子和纤维方向通过移位算子I - ζb随厚度变化，不变量继承该依赖性。拉伸-压缩分裂、通道退化、平面应力凝聚、一致切线和有限元组装均在通道势及其导数中表达，允许闭式或学习算子。纤维横向相互作用能存储一次，并通过其耦合的机制场的乘积退化。六个条件定义可容许算子；两个线性不变量被证明在变形梯度上是凸的，几何切线被证明独立于材料切线，且平面应力凝聚在残余刚度为正的地方是正则的。三层协议认证代数、求解器状态以及状态作为训练数据的准入。对带缺口的IM7/8552壳体的数值研究验证了薄和弯曲状态下的离散化，并表明纤维取向控制损伤包络和承载能力，而曲率驱动了单一中面场无法表示的厚度方向断裂不对称性。
英文摘要
Phase-field models of fracture in fibre-reinforced shells are usually formulated against a single closed-form stored energy, so that the stress, consistent tangent and plane-stress condensation are derived and verified for that expression alone. Here the constitutive law enters instead as a replaceable operator. The Green-Lagrange strain of a geometrically exact Reissner-Mindlin shell is pulled back through the Cholesky factor of the reference metric and resolved on four mutually orthogonal invariants with an exact closure identity, making the separation into fibre, inter-fibre and interaction channels a change of basis rather than a modelling assumption. On a curved midsurface, the metric, Cholesky factor and fibre direction vary through the thickness through the shifter I - zeta b, and the invariants inherit that dependence. The tension-compression split, channel degradation, plane-stress condensation, consistent tangent and finite-element assembly are all expressed in the channel potentials and their derivatives, allowing either closed-form or learned operators. The fibre-transverse interaction energy is stored once and degraded by the product of the fields whose mechanisms it couples. Six conditions define admissible operators; the two linear invariants are proved convex in the deformation gradient, the geometric tangent is shown independent of the material tangent, and the plane-stress condensation is regular wherever the residual stiffness is positive. A three-tier protocol certifies the algebra, solver state and admission of a state as training data. Numerical studies on notched IM7/8552 shells verify the discretisation in thin and curved regimes and show that fibre orientation governs the damage envelope and load capacity, while curvature drives a through-thickness fracture asymmetry that a single midsurface field cannot represent.
Comments36 pages, 15 figures, 1 table
